Which machine learning models are universal function approximators?
Support vector machines
In the paper A Note on the Universal Approximation Capability of Support Vector Machines (2002) B. Hammer and K. Gersmann investigate the universal function approximation capabilities of SVMs. More specifically, the authors show that SVMs with standard kernels (including Gaussian, polynomial, and several dot product kernels) can approximate any measurable or continuous function up to any desired accuracy. Therefore, SVMs are universal function approximators.
Polynomials
It is also widely known that we can approximate any continuous function with polynomials (see the Stone-Weierstrass theorem). You can use polynomial regression to fit polynomials to your labelled data.